A certain factory produces and sells $8000$ cars per month, making a monthly net profit of $P$ dollars. They sell each car for $n$ dollars and it costs them $c$ dollars to produce a single car. Write an equation that relates $P$, $n$, and $c$.
Solution: The factory's net profit is equal to the factory's total income, reduced by the factory's total expenses. What is the factory's income from producing and selling $8000$ cars? What are the expenses? The income is $8000n$ dollars: $\begin{aligned} &\phantom{=}\left(n\,\dfrac{\text{dollars}}{\text{car}}\right)\left(8000\,\text{cars}\right) \\\\ &=n\cdot 8000\,\dfrac{\text{dollars}}{\cancel\text{car}}\cdot\,\cancel\text{cars} \\\\ &=8000n\,\text{dollars} \end{aligned}$ Similarly, the expenses are $8000c$ dollars. The net profit is then $8000n$ minus $8000c$ : $8000n-8000c=P$ This can also be written as $8000(n-c)=P$.